Question: The fastest growing plant on record is a Hesperoyucca whipplei that grew 3.7 m in 14 days. What was its growth rate in micrometers per second?

The height by which the plant grew, h=3.7 m

The time taken by the plant to grow, t = 14 days

The growth rate is the rate of change in height of the plant and is a function of time.To find the rate of growth the height of the plant is to be measured with respect to time.

The expression for the growth rate is given as follows:

$growthrate=\frac{h}{t}$ … (i)

Here,h is the growth in height and t is the time.

Convert the growth of the plant (h) into micrometers and days (t) in seconds.

$$\begin{gathered} h=3.7m\times \frac{{10}^6\mu m}{m} \\ =3.7\times {10}^6\mu m \\ t=14days\times \left(\frac{24hour}{day}\right)\times \left(\frac{60min}{hr}\right)\times \left(\frac{60s}{min}\right) \\ =1,250.600s \end{gathered}$$

Thus, $3.7\times {10}^6$the height is and timespan is 1,250,600s.

Using equation (i), the growth rate of plant is calculated as:

$$\begin{gathered} growthrate=\frac{h}{t} \\ =\frac{3.7\times {10}^6\mu m}{1209600s} \\ =3.1\mu m/s \end{gathered}$$

Thus, the growth rate of plants is$3.1\mu m/s$